Ancient calendars were based on the lunar cycle until Julius Caesar imposed his solar calendar throughout the Roman Empire. By losing the link with the moon, the Julian calendar gained about three days per 400 years. In the 16th C, the discrepancy between the calendar dates of the solstices and their actual occurrence became a concern to Christians … the formula for dating Easter depended upon the lunar cycle and the vernal equinox. Easter was being celebrated on the wrong date!
In 1582 Pope Gregory XIII endorsed the recommendations of his astronomers and mathematicians. The new Gregorian Calendar changed leap-year rules and … to adjust for the accumulated discrepancy … the year 1582 was shortened by 10 days. The days between October 4th and 15th were abolished!
The 16th C was the era of the Protestant Reformation, and papal decrees carried little weight with non-Catholic Christians, so Gregory’s calendar reform was not soon adopted in Protestant countries. By the time Britain adopted the new calendar in 1752, an eleventh day had to be dropped. Russia didn’t adopt it until the 20th C, which explains why the October Revolution of 1917 actually occurred in November!
The Greek Orthodox Church has never endorsed the Gregorian Reform of the Calendar, so Orthodox Christmas and Easter fall some days later than the same celebrations in the Latin Church.